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Preface
List of Symbols
Group Representations
Fundamental Concepts
Matrix Representations
G-modules and the Group Algebra
Reducibility
Complete Reducibility and Maschke's Theorem
G-homomorphisms and Schur’s Lemma
Commutant and Endomorphism Algebras
Group Characters
Inner Products of Characters
Decomposition of the Group Algebra
Tensor Products Again
Restricted and Induced Representations
Exercises
Representations of the Symmetric Group
Young Subgroups, Tableaux, and Tabloids
Dominance and Lexicographic Ordering
Specht Modules
The Submodule Theorem
Standard Tableaux and a Basis for S^lambda
Garnir Elements
Young’s Natural Representation
The Branching Rule
The Decomposition of M^mu
The Semistandard Basis for Hom(S^lambda, M^mu)
Kostka Numbers and Young’s Rule
Exercises
Combinatorial Algorithms
The Hook Formula
The Determinantal Formula
The Robinson-Schensted Algorithm
Column Insertion
Increasing and Decreasing Subsequences
The Knuth Relations
Subsequences Again
Viennot’s Geometric Construction
Schützenberger’s Jeu de Taquin
Dual Equivalence
Evacuation
Exercises
Symmetric Functions
Introduction to Generating Functions
The Hillman-Grassl Algorithm
The Ring of Symmetric Functions
Schur Functions
The Jacobi-Trudi Determinants
Other Definitions of the Schur Function
The Characteristic Map
Knuth’s Algorithm
The Littlewood-Richardson Rule
The Murnaghan-Nakayama Rule
Exercises
Bibliography
Index